Kelly Renee Gissendaner was pronounced dead by injection of pentobarbitone at the state prison in Jackson. She was convicted of murder over the February 1997 killing of her husband after she conspired with her lover, who stabbed Douglas Gissendaner to death.

The 47-year-old sobbed as she said she loved her children and apologised to Mr Gissendaner's family, saying she hoped they could find some peace and happiness. She also addressed her lawyer, Susan Casey.

"I just want to say God bless you all and I love you, Susan. You let my kids know I went out singing Amazing Grace," Gissendaner said.

As well as Amazing Grace, Gissendaner also appeared to sing another song before taking several deep breaths and then becoming still.

More than 100 people gathered in rainy conditions outside the prison to support her. Among them was Rev Della Bacote, a chaplain at Saint Thomas Hospital in Nashville, who spent several hours with Gissendaner on Tuesday afternoon, talking and praying.

"She was at peace with whatever was to come," Rev Bacote said.

Gissendaner's three children visited her on Monday but were not able to see her on Tuesday because they were giving evidence to the Georgia Board of Pardons and Paroles, Rev Bacote said.

Two of Gissendaner's three children had previously addressed the board and also put out a video earlier this month pleading for their mother's life and talking about their own difficult path to forgiveness. Her oldest son had not previously addressed the board.

Various courts, including the US Supreme Court, denied multiple last-ditch efforts to stop her execution, and the parole board stood by its February decision to deny clemency.

Pope Francis's diplomatic representative in the US, Archbishop Carlo Maria Vigano, had sent a letter to the parole board on behalf of the pontiff asking for a commutation of Gissendaner's sentence "to one that would better express both justice and mercy".

He cited an address the Pope made to a joint session of Congress last week in which he called for the abolition of the death penalty.

Gissendaner's lawyers also submitted a statement from former Georgia Supreme Court Chief Justice Norman Fletcher to the parole board, who argued that Gissendaner's death sentence was not proportionate to her role in the crime.

Her lover, Gregory Owen, who carried out the fatal stabbing, is serving a life sentence and will become eligible for parole in 2022.

Mr Fletcher also noted that Georgia had not executed a person who had not actually committed a killing since the US Supreme Court reinstated the death penalty in 1976.

Gissendaner's lawyers also said she was a seriously damaged woman who had undergone a spiritual transformation in prison and had been a model prisoner who had shown remorse.

But Mr Gissendaner's family said in a statement that he was the victim and that his wife received an appropriate sentence.

"As the murderer, she's been given more rights and opportunity over the last 18 years than she ever afforded to Doug who, again, is the victim here," the statement said. "She had no mercy, gave him no rights, no choices, nor the opportunity to live his life."

Gissendaner repeatedly pushed Owen in late 1996 to kill her husband rather than just divorcing him as Owen suggested, prosecutors have said.

Acting on her instructions, Owen ambushed Douglas Gissendaner at Gissendaner's home, forced him to drive to a remote area and stabbed him multiple times, prosecutors said.